libMesh::DenseMatrixBase< T > Class Template Reference

Defines an abstract dense matrix base class for use in Finite Element-type computations. More...

#include <dense_matrix_base.h>

Inheritance diagram for libMesh::DenseMatrixBase< T >:

Public Member Functions
	DenseMatrixBase (DenseMatrixBase &&)=default
	The 5 special functions can be defaulted for this class, as it does not manage any memory itself.
	DenseMatrixBase (const DenseMatrixBase &)=default
DenseMatrixBase &	operator= (const DenseMatrixBase &)=default
DenseMatrixBase &	operator= (DenseMatrixBase &&)=default
virtual	~DenseMatrixBase ()=default
virtual void	zero ()=0
	Set every element in the matrix to 0.
virtual T	el (const unsigned int i, const unsigned int j) const =0
virtual T &	el (const unsigned int i, const unsigned int j)=0
virtual void	left_multiply (const DenseMatrixBase< T > &M2)=0
	Performs the operation: (*this) <- M2 * (*this)
virtual void	right_multiply (const DenseMatrixBase< T > &M3)=0
	Performs the operation: (*this) <- (*this) * M3.
unsigned int	m () const
unsigned int	n () const
void	print (std::ostream &os=libMesh::out) const
	Pretty-print the matrix, by default to libMesh::out.
void	print_scientific (std::ostream &os, unsigned precision=8) const
	Prints the matrix entries with more decimal places in scientific notation.
template<typename T2 , typename T3 >
std::enable_if< ScalarTraits< T2 >::value, void >::type	add (const T2 factor, const DenseMatrixBase< T3 > &mat)
	Adds factor to every element in the matrix.
DenseVector< T >	diagonal () const
	Return the matrix diagonal.

Protected Member Functions
	DenseMatrixBase (const unsigned int new_m=0, const unsigned int new_n=0)
	Constructor.
void	condense (const unsigned int i, const unsigned int j, const T val, DenseVectorBase< T > &rhs)
	Condense-out the (i,j) entry of the matrix, forcing it to take on the value val.

Static Protected Member Functions
static void	multiply (DenseMatrixBase< T > &M1, const DenseMatrixBase< T > &M2, const DenseMatrixBase< T > &M3)
	Helper function - Performs the computation M1 = M2 * M3 where: M1 = (m x n) M2 = (m x p) M3 = (p x n)

Protected Attributes
unsigned int	_m
	The row dimension.
unsigned int	_n
	The column dimension.

Friends
std::ostream &	operator<< (std::ostream &os, const DenseMatrixBase< T > &m)
	Formatted print as above but allows you to do DenseMatrix K; libMesh::out << K << std::endl;.

Detailed Description

template<typename T>
class libMesh::DenseMatrixBase< T >

Defines an abstract dense matrix base class for use in Finite Element-type computations.

Specialized dense matrices, for example DenseSubMatrices, can be derived from this class.

Author

John W. Peterson

Date

2003

Definition at line 46 of file dense_matrix_base.h.

Constructor & Destructor Documentation

DenseMatrixBase() [1/3]

template<typename T >

libMesh::DenseMatrixBase< T >::DenseMatrixBase ( const unsigned int  new_m = 0, const unsigned int  new_n = 0  )

inlineprotected

Constructor.

Creates a dense matrix of dimension m by n. Protected so that there is no way the user can create one.

Definition at line 54 of file dense_matrix_base.h.

                                              : _m(new_m), _n(new_n) {}

DenseMatrixBase() [2/3]

template<typename T >

libMesh::DenseMatrixBase< T >::DenseMatrixBase ( DenseMatrixBase< T > &&  )

default

The 5 special functions can be defaulted for this class, as it does not manage any memory itself.

DenseMatrixBase() [3/3]

template<typename T >

libMesh::DenseMatrixBase< T >::DenseMatrixBase ( const DenseMatrixBase< T > &  )

default

~DenseMatrixBase()

template<typename T >

virtual libMesh::DenseMatrixBase< T >::~DenseMatrixBase ( )

virtualdefault

Member Function Documentation

add()

template<typename T >

template<typename T2 , typename T3 >

std::enable_if< ScalarTraits< T2 >::value, void >::type libMesh::DenseMatrixBase< T >::add ( const T2  factor, const DenseMatrixBase< T3 > &  mat  )

inline

Adds factor to every element in the matrix.

This should only work if T += T2 * T3 is valid C++ and if T2 is scalar. Return type is void

Definition at line 195 of file dense_matrix_base.h.

{
  libmesh_assert_equal_to (this->m(), mat.m());
  libmesh_assert_equal_to (this->n(), mat.n());
 
  for (auto j : make_range(this->n()))
    for (auto i : make_range(this->m()))
      this->el(i,j) += factor*mat.el(i,j);
}

References libMesh::DenseMatrixBase< T >::el(), libMesh::DenseMatrixBase< T >::m(), libMesh::make_range(), and libMesh::DenseMatrixBase< T >::n().

condense()

template<typename T >

void libMesh::DenseMatrixBase< T >::condense ( const unsigned int  i, const unsigned int  j, const T  val, DenseVectorBase< T > &  rhs  )

protected

Condense-out the (i,j) entry of the matrix, forcing it to take on the value val.

This is useful in numerical simulations for applying boundary conditions. Preserves the symmetry of the matrix.

Definition at line 73 of file dense_matrix_base_impl.h.

  {
    libmesh_assert_equal_to (this->_m, rhs.size());
    libmesh_assert_equal_to (iv, jv);
 
 
    // move the known value into the RHS
    // and zero the column
    for (auto i : make_range(this->m()))
      {
        rhs.el(i) -= this->el(i,jv)*val;
        this->el(i,jv) = 0.;
      }
 
    // zero the row
    for (auto j : make_range(this->n()))
      this->el(iv,j) = 0.;
 
    this->el(iv,jv) = 1.;
    rhs.el(iv) = val;
 
  }

References libMesh::DenseVectorBase< T >::el(), libMesh::make_range(), and libMesh::DenseVectorBase< T >::size().

Referenced by libMesh::DenseMatrix< T >::condense().

diagonal()

template<typename T >

DenseVector< T > libMesh::DenseMatrixBase< T >::diagonal

(

)

const

Return the matrix diagonal.

Definition at line 37 of file dense_matrix_base_impl.h.

  {
    DenseVector<T> ret(_m);
    for (decltype(_m) i = 0; i < _m; ++i)
      ret(i) = el(i, i);
    return ret;
  }

Referenced by libMesh::DiagonalMatrix< T >::add_matrix().

el() [1/2]

template<typename T >

virtual T libMesh::DenseMatrixBase< T >::el ( const unsigned int  i, const unsigned int  j  ) const

pure virtual

Returns

The (i,j) element of the matrix. Since internal data representations may differ, you must redefine this function.

Implemented in libMesh::DenseMatrix< T >, libMesh::DenseMatrix< Number >, libMesh::DenseMatrix< Real >, and libMesh::DenseSubMatrix< T >.

Referenced by libMesh::DenseMatrixBase< T >::add(), and libMesh::DenseMatrixBase< T >::multiply().

el() [2/2]

template<typename T >

virtual T & libMesh::DenseMatrixBase< T >::el ( const unsigned int  i, const unsigned int  j  )

pure virtual

Returns

The (i,j) element of the matrix as a writable reference. Since internal data representations may differ, you must redefine this function.

Implemented in libMesh::DenseMatrix< T >, libMesh::DenseMatrix< Number >, libMesh::DenseMatrix< Real >, and libMesh::DenseSubMatrix< T >.

left_multiply()

template<typename T >

virtual void libMesh::DenseMatrixBase< T >::left_multiply ( const DenseMatrixBase< T > &  M2 )

pure virtual

Performs the operation: (*this) <- M2 * (*this)

Implemented in libMesh::DenseMatrix< Number >, libMesh::DenseMatrix< Real >, libMesh::DenseMatrix< T >, and libMesh::DenseSubMatrix< T >.

m()

template<typename T >

unsigned int libMesh::DenseMatrixBase< T >::m ( ) const

inline

Returns

The row-dimension of the matrix.

Definition at line 104 of file dense_matrix_base.h.

{ return _m; }

References libMesh::DenseMatrixBase< T >::_m.

Referenced by libMesh::DenseMatrix< T >::_left_multiply_transpose(), libMesh::DenseMatrix< T >::_multiply_blas(), libMesh::DenseMatrix< T >::_right_multiply_transpose(), libMesh::DenseMatrix< T >::_svd_solve_lapack(), libMesh::DenseMatrix< T >::add(), libMesh::DenseMatrixBase< T >::add(), libMesh::PetscMatrix< T >::add_block_matrix(), libMesh::StaticCondensation::add_matrix(), libMesh::DiagonalMatrix< T >::add_matrix(), libMesh::EigenSparseMatrix< T >::add_matrix(), libMesh::LaspackMatrix< T >::add_matrix(), libMesh::PetscMatrix< T >::add_matrix(), libMesh::EpetraMatrix< T >::add_matrix(), libMesh::RBConstruction::add_scaled_matrix_and_vector(), libMesh::DofMap::build_constraint_matrix(), libMesh::DofMap::build_constraint_matrix_and_vector(), libMesh::DofMap::extract_local_vector(), libMesh::DenseMatrix< T >::get_transpose(), libMesh::DofMap::heterogeneously_constrain_element_jacobian_and_residual(), libMesh::DofMap::heterogeneously_constrain_element_residual(), libMesh::isfinite(), libMesh::isfinite(), libMesh::isinf(), libMesh::isinf(), libMesh::isnan(), libMesh::isnan(), libMesh::DenseMatrix< T >::left_multiply(), libMesh::DenseMatrix< T >::left_multiply(), libMesh::DofMap::max_constraint_error(), libMesh::DenseMatrixBase< T >::multiply(), libMesh::PatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::DenseMatrix< T >::operator=(), libMesh::RBEIMEvaluation::set_interpolation_matrix_entry(), DualShapeTest::testEdge2Lagrange(), DenseMatrixTest::testEVD_helper(), DenseMatrixTest::testSVD(), and MetaPhysicL::RawType< libMesh::DenseMatrix< T > >::value().

multiply()

template<typename T >

void libMesh::DenseMatrixBase< T >::multiply ( DenseMatrixBase< T > &  M1, const DenseMatrixBase< T > &  M2, const DenseMatrixBase< T > &  M3  )

staticprotected

Helper function - Performs the computation M1 = M2 * M3 where: M1 = (m x n) M2 = (m x p) M3 = (p x n)

Definition at line 46 of file dense_matrix_base_impl.h.

  {
    // Assertions to make sure we have been
    // passed matrices of the correct dimension.
    libmesh_assert_equal_to (M1.m(), M2.m());
    libmesh_assert_equal_to (M1.n(), M3.n());
    libmesh_assert_equal_to (M2.n(), M3.m());
 
    const unsigned int m_s = M2.m();
    const unsigned int p_s = M2.n();
    const unsigned int n_s = M1.n();
 
    // Do it this way because there is a
    // decent chance (at least for constraint matrices)
    // that M3(k,j) = 0. when right-multiplying.
    for (unsigned int k=0; k<p_s; k++)
      for (unsigned int j=0; j<n_s; j++)
        if (M3.el(k,j) != 0.)
          for (unsigned int i=0; i<m_s; i++)
            M1.el(i,j) += M2.el(i,k) * M3.el(k,j);
  }

References libMesh::DenseMatrixBase< T >::el(), libMesh::DenseMatrixBase< T >::m(), and libMesh::DenseMatrixBase< T >::n().

n()

template<typename T >

unsigned int libMesh::DenseMatrixBase< T >::n ( ) const

inline

Returns

The column-dimension of the matrix.

Definition at line 109 of file dense_matrix_base.h.

{ return _n; }

References libMesh::DenseMatrixBase< T >::_n.

Referenced by libMesh::DenseMatrix< T >::_left_multiply_transpose(), libMesh::DenseMatrix< T >::_multiply_blas(), libMesh::DenseMatrix< T >::_right_multiply_transpose(), libMesh::DenseMatrix< T >::_svd_solve_lapack(), libMesh::DenseMatrix< T >::add(), libMesh::DenseMatrixBase< T >::add(), libMesh::PetscMatrix< T >::add_block_matrix(), libMesh::StaticCondensation::add_matrix(), libMesh::DiagonalMatrix< T >::add_matrix(), libMesh::EigenSparseMatrix< T >::add_matrix(), libMesh::LaspackMatrix< T >::add_matrix(), libMesh::PetscMatrix< T >::add_matrix(), libMesh::EpetraMatrix< T >::add_matrix(), libMesh::RBConstruction::add_scaled_matrix_and_vector(), libMesh::DofMap::build_constraint_matrix(), libMesh::DofMap::build_constraint_matrix_and_vector(), libMesh::DofMap::constrain_element_residual(), libMesh::DofMap::extract_local_vector(), libMesh::DenseMatrix< T >::get_transpose(), libMesh::DofMap::heterogeneously_constrain_element_jacobian_and_residual(), libMesh::DofMap::heterogeneously_constrain_element_residual(), libMesh::isfinite(), libMesh::isfinite(), libMesh::isinf(), libMesh::isinf(), libMesh::isnan(), libMesh::isnan(), libMesh::DenseMatrix< T >::left_multiply(), libMesh::DenseMatrix< T >::left_multiply(), libMesh::DofMap::max_constraint_error(), libMesh::DenseMatrixBase< T >::multiply(), libMesh::PatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::WeightedPatchRecoveryErrorEstimator::EstimateError::operator()(), libMesh::DenseMatrix< T >::operator=(), libMesh::DenseMatrix< Real >::right_multiply(), libMesh::RBEIMEvaluation::set_interpolation_matrix_entry(), DualShapeTest::testEdge2Lagrange(), DenseMatrixTest::testSVD(), and MetaPhysicL::RawType< libMesh::DenseMatrix< T > >::value().

operator=() [1/2]

template<typename T >

DenseMatrixBase & libMesh::DenseMatrixBase< T >::operator= ( const DenseMatrixBase< T > &  )

default

operator=() [2/2]

template<typename T >

DenseMatrixBase & libMesh::DenseMatrixBase< T >::operator= ( DenseMatrixBase< T > &&  )

default

print()

template<typename T >

void libMesh::DenseMatrixBase< T >::print

(

std::ostream &

os = libMesh::out

)

const

Pretty-print the matrix, by default to libMesh::out.

Definition at line 125 of file dense_matrix_base_impl.h.

  {
    for (auto i : make_range(this->m()))
      {
        for (auto j : make_range(this->n()))
          os << std::setw(8)
             << this->el(i,j) << " ";
 
        os << std::endl;
      }
 
    return;
  }

References libMesh::make_range().

print_scientific()

template<typename T >

void libMesh::DenseMatrixBase< T >::print_scientific	(	std::ostream &	os,
		unsigned	precision = 8
	)		const

Prints the matrix entries with more decimal places in scientific notation.

Definition at line 101 of file dense_matrix_base_impl.h.

  {
    // save the initial format flags
    std::ios_base::fmtflags os_flags = os.flags();
 
    // Print the matrix entries.
    for (auto i : make_range(this->m()))
      {
        for (auto j : make_range(this->n()))
          os << std::setw(15)
             << std::scientific
             << std::setprecision(precision)
             << this->el(i,j) << " ";
 
        os << std::endl;
      }
 
    // reset the original format flags
    os.flags(os_flags);
  }

References libMesh::make_range().

right_multiply()

template<typename T >

virtual void libMesh::DenseMatrixBase< T >::right_multiply ( const DenseMatrixBase< T > &  M3 )

pure virtual

Performs the operation: (*this) <- (*this) * M3.

Implemented in libMesh::DenseMatrix< Number >, libMesh::DenseMatrix< Real >, libMesh::DenseMatrix< T >, and libMesh::DenseSubMatrix< T >.

zero()

template<typename T >

virtual void libMesh::DenseMatrixBase< T >::zero ( )

pure virtual

Set every element in the matrix to 0.

You must redefine what you mean by zeroing the matrix since it depends on how your values are stored.

Implemented in libMesh::DenseMatrix< T >, libMesh::DenseMatrix< Number >, libMesh::DenseMatrix< Real >, and libMesh::DenseSubMatrix< T >.

Friends And Related Symbol Documentation

operator<<

template<typename T >

std::ostream & operator<< ( std::ostream &  os, const DenseMatrixBase< T > &  m  )

friend

Formatted print as above but allows you to do DenseMatrix K; libMesh::out << K << std::endl;.

Definition at line 121 of file dense_matrix_base.h.

  {
    m.print(os);
    return os;
  }

Member Data Documentation

_m

template<typename T >

unsigned int libMesh::DenseMatrixBase< T >::_m

protected

The row dimension.

Definition at line 176 of file dense_matrix_base.h.

Referenced by libMesh::DenseMatrixBase< T >::m(), libMesh::DenseMatrix< T >::sub_matrix(), and libMesh::DenseMatrix< T >::swap().

_n

template<typename T >

unsigned int libMesh::DenseMatrixBase< T >::_n

protected

The column dimension.

Definition at line 181 of file dense_matrix_base.h.

Referenced by libMesh::DenseMatrixBase< T >::n(), libMesh::DenseMatrix< T >::sub_matrix(), and libMesh::DenseMatrix< T >::swap().

---

The documentation for this class was generated from the following files:

• include/numerics/dense_matrix_base.h
• include/numerics/dense_matrix_base_impl.h